Any state could chose that method (along with all "at large") at anytime they wished. I had that thought earlier this week with the "VA" vote. Effectively what Virginians have chosen is for all seats to be elected by a statewide vote.
Virginians haven't made them be by statewide vote; even with as strong as they gerrymandered things, the prediction is they'd end up with 10 Democratic districts and 1 Republican district, meaning it's 10-1. An at-large election, if won by Democrats, would be 11-0 (an at-large election would also carry the risk that Republicans could somehow eke out a win in a statewide election in which case they'd get all 11 seats).
However, states can't do at-large elections or proportional representation even if they wanted to, because that's forbidden by federal law. Behold
2 U.S. Code § 2c:
In each State entitled in the Ninety-first Congress or in any subsequent Congress thereafter to more than one Representative under an apportionment made pursuant to the provisions of section 2a(a) of this title, there shall be established by law a number of districts equal to the number of Representatives to which such State is so entitled, and Representatives shall be elected only from districts so established, no district to elect more than one Representative (except that a State which is entitled to more than one Representative and which has in all previous elections elected its Representatives at Large may elect its Representatives at Large to the Ninety-first Congress).
The 91st Congress was 1969-1971, if anyone is curious. As one can see, this requires states to have single-member electoral districts for the House of Representatives. At-large elections as well as proportional representation (even a mixture of proportional representation and single-member districts) are therefore prohibited. For a state to set that up, this law would need to be changed. Which, of course, Congress can do. Congress could not only choose to allow at-large elections and proportional representation, but it could
require states to do either for the House of Representatives if it passed a law doing so. However, until such time as this law is changed, states are required to have single-member districts for the House.
A state is fully free to have their
own legislature be done via at-large or proportional representation, though, and Congress can neither require nor prohibit any manner of election of them, beyond any rules that are already in the Constitution. As far as I'm aware, though, all states use single-member districts for their legislature.
One thing I'm not sure about is whether Congress can do a
nationwide proportional representation vote by law. It definitely can require proportional representation within each state (i.e. if one state has 40% vote for a party, 40% of the seats for that state go to that party), but I'm not sure if they can have votes in one state affect the Representatives from another state, which is what a
national proportional vote would do (i.e. if 40% of the country votes for a particular party, 40% of seats go to that party). That one would probably require an amendment. But proportional representation
within each state could be required by a federal law.